Robust Kernel Approximation for Classification

This paper investigates a robust kernel approximation scheme for support vector machine classification with indefinite kernels. It aims to tackle the issue that the indefinite kernel is contaminated by noises and outliers, i.e. a noisy observation of the true positive definite (PD) kernel. The traditional algorithms recovery the PD kernel from the observation with the small Gaussian noises, however, such way is not robust to noises and outliers that do not follow a Gaussian distribution. In this paper, we assume that the error is subject to a Gaussian-Laplacian distribution to simultaneously dense and sparse/abnormal noises and outliers. The derived optimization problem including the kernel learning and the dual SVM classification can be solved by an alternate iterative algorithm. Experiments on various benchmark data sets show the robustness of the proposed method when compared with other state-of-the-art kernel modification based methods.